Math Problem Statement

3√5 × 3√5 × 2√6

Solution

The expression in the image is:

35×35×263\sqrt{5} \times 3\sqrt{5} \times 2\sqrt{6}

Let's simplify this step-by-step:

  1. Group the constants and the square roots separately: (3×3×2)×(5×5×6)(3 \times 3 \times 2) \times (\sqrt{5} \times \sqrt{5} \times \sqrt{6})

  2. Multiply the constants: 3×3×2=183 \times 3 \times 2 = 18

  3. Multiply the square roots: 5×5=5\sqrt{5} \times \sqrt{5} = 5 So now you have: 5×6=565 \times \sqrt{6} = 5\sqrt{6}

  4. Multiply everything together: 18×56=90618 \times 5\sqrt{6} = 90\sqrt{6}

So, the simplified result is:

90690\sqrt{6}

Would you like further details or explanations on any step?

Here are five related questions for practice:

  1. What is (23)×(412)(2\sqrt{3}) \times (4\sqrt{12})?
  2. Simplify the expression 8×2\sqrt{8} \times \sqrt{2}.
  3. What is the product of 57×375\sqrt{7} \times 3\sqrt{7}?
  4. How do you multiply two expressions involving square roots, like 2×18\sqrt{2} \times \sqrt{18}?
  5. What is the result of 610×256\sqrt{10} \times 2\sqrt{5}?

Tip: When multiplying square roots, remember that a×b=a×b\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radical Expressions
Multiplication of Square Roots

Formulas

√a × √b = √(a × b)
Multiplication of constants

Theorems

Product of Square Roots

Suitable Grade Level

Grades 8-10